Apparatus and method for controlling product grade changes in a paper machine or other machine

ABSTRACT

A paper machine includes equipment for processing or producing a product in a continuous manner, such as a paper sheet. A grade change occurs when the equipment transitions from producing or processing a product having a first grade to producing or processing a product having a second grade. To support the grade change, a target for at least one controlled variable and a target for at least one manipulated variable are identified. The at least one manipulated variable and the at least one controlled variable are associated with the production of the product. A trajectory for the at least one manipulated variable and a corresponding trajectory for the at least one controlled variable are identified using the targets. The grade change is implemented using the trajectories so as to transition from production of the product having the first grade to production of the product having the second grade.

TECHNICAL FIELD

This disclosure relates generally to control systems and morespecifically to an apparatus and method for controlling product gradechanges in a paper machine or other machine.

BACKGROUND

Various systems are available and used to manufacture sheets of paperand other sheet products. The sheets of material often have multiplecharacteristics that are monitored and controlled during themanufacturing process, such as dry weight, moisture, and caliper(thickness). The control of these or other sheet properties in asheet-making machine is typically concerned with keeping the sheetproperties as close as possible to target or desired values.

Sheet-making machines are often capable of producing sheets of materialhaving different grades. For example, paper grades are typicallyassociated with different characteristics of paper sheets. Some exampletypes of paper grades include bond, book, label, and newsprint grades.Many sheet-making machines are also capable of transitioning from theproduction of one grade of material to the production of another gradeof material in a continuous fashion. In other words, the sheet-makingmachines continue producing a sheet of material, but the grade of thesheet changes during the production. As a result, the sheet-makingmachines do not need to be shut down and restarted in order to changethe grade of the sheet being produced.

In many instances, a grade change frequently results in productionlosses, meaning the sheet of material produced during the grade changeis often unmarketable. This is typically due to the sheet having one ormore undesirable characteristics, which are caused by altering theproduction process to change the grade of the sheet being produced. Thistypically results in a waste of material and a loss of revenue.

SUMMARY

This disclosure provides an apparatus and method for controlling productgrade changes in a paper machine or other machine.

In a first embodiment, a method includes identifying a target for atleast one controlled variable and a target for at least one manipulatedvariable. The at least one manipulated variable and the at least onecontrolled variable are associated with production of a product. Themethod also includes identifying a trajectory for the at least onemanipulated variable and a corresponding trajectory for the at least onecontrolled variable. The trajectories are identified using the targets.In addition, the method includes implementing a grade change using thetrajectories so as to transition from production of the product having afirst grade to production of the product having a second grade.

In particular embodiments, the product includes a paper sheet producedby a paper machine. The at least one controlled variable includes a dryweight of the paper sheet, an ash content of the paper sheet, and/or amoisture content of the paper sheet. The at least one manipulatedvariable includes a thick stock flow, a filler flow, a steam pressureassociated with a dryer section in the paper machine, and/or a machinespeed associated with the paper machine.

In other particular embodiments, identifying the target for the at leastone controlled variable includes using a recipe associated with thesecond grade. Also, identifying the target for the at least onemanipulated variable includes using the target for the at least onecontrolled variable.

In still other particular embodiments, identifying the trajectoriesincludes performing an iterative process. The iterative process includescalculating values for the at least one manipulated variable, where thevalues form the trajectory for the at least one manipulated variable.The iterative process also includes calculating corresponding values forthe at least one controlled variable, where the values form thetrajectory for the at least one controlled variable. The iterativeprocess further includes updating a process model used to identify thecorresponding values for the at least one controlled variable. Inaddition, the iterative process includes repeating the calculating andupdating steps until at least stop condition occurs.

In a second embodiment, an apparatus includes at least one processoroperable to identify a target for at least one controlled variable and atarget for at least one manipulated variable. The at least onemanipulated variable and the at least one controlled variable areassociated with production of a product. The at least one processor isalso operable to identify a trajectory for the at least one manipulatedvariable and a corresponding trajectory for the at least one controlledvariable using the targets. The at least one processor is furtheroperable to implement a grade change using the trajectories so as totransition from production of the product having a first grade toproduction of the product having a second grade. The apparatus alsoincludes at least one memory operable to store the targets and thetrajectories.

In a third embodiment, a computer program is embodied on a computerreadable medium. The computer program includes computer readable programcode for identifying a target for at least one controlled variable and atarget for at least one manipulated variable. The at least onemanipulated variable and the at least one controlled variable areassociated with production of a product. The computer program alsoincludes computer readable program code for identifying a trajectory forthe at least one manipulated variable and a corresponding trajectory forthe at least one controlled variable. The trajectories are identifiedusing the targets. In addition, the computer program includes computerreadable program code for implementing a grade change using thetrajectories so as to transition from production of the product having afirst grade to production of the product having a second grade.

In a fourth embodiment, a system includes a paper machine operable toproduce a paper sheet having multiple grades. The system also includes acontroller operable to initiate a transition from a first grade to asecond grade. The controller is operable to identify a target for atleast one controlled variable and a target for at least one manipulatedvariable. The controller is also operable to identify a trajectory forthe at least one manipulated variable and a corresponding trajectory forthe at least one controlled variable using the targets. In addition, thecontroller is operable to implement the grade change using thetrajectories so as to transition from production of the paper sheethaving the first grade to production of the product having the secondgrade.

Other technical features may be readily apparent to one skilled in theart from the following figures, descriptions, and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this disclosure, reference is nowmade to the following description, taken in conjunction with theaccompanying drawings, in which:

FIGS. 1A and 1B illustrate an example paper production system inaccordance with this disclosure;

FIGS. 2A and 2B illustrate example grade change control models inaccordance with this disclosure;

FIG. 3 illustrates example tasks during a grade change in accordancewith this disclosure;

FIG. 4 illustrates an example grade change controller in accordance withthis disclosure;

FIG. 5 illustrates an example method for grade change control inaccordance with this disclosure; and

FIGS. 6 through 9 illustrate example methods performed by a particularimplementation of a grade change controller in accordance with thisdisclosure.

DETAILED DESCRIPTION

FIGS. 1A and 1B illustrate an example paper production system 100according to one embodiment of this disclosure. The embodiment of thepaper production system 100 shown in FIGS. 1A and 1B is for illustrationonly. Other embodiments of the paper production system 100 may be usedwithout departing from the scope of this disclosure.

As shown in FIG. 1A, the paper production system 100 includes a papermachine 102. The paper machine 102 includes various components used toproduce or process a paper product. In this example, the variouscomponents may be used to produce a paper sheet 104 collected at a reel106.

In this example embodiment, the paper machine 102 includes a headbox108, which distributes a pulp suspension uniformly across the machineonto a continuous moving screen or mesh 110. The pulp suspensionentering the headbox 108 may contain, for example, 0.2-3% wood fibersand possibly other solids, with the remainder of the suspension beingwater. The headbox 108 includes any suitable structure for distributinga pulp suspension. The headbox 108 may, for example, include a sliceopening through which the pulp suspension is distributed onto the screenor mesh 110. The screen or mesh 110 represents any suitable structurefor receiving a pulp suspension and allowing water or other materials todrain or leave the pulp suspension.

The sheet 104 then enters a press section 112, which includes multiplepress rolls. The sheet 104 travels through the openings (referred to as“nips”) between pairs of counter-rotating rolls in the press section112. In this way, the rolls in the press section 112 compress the pulpmaterial forming the sheet 104. This may help to remove more water fromthe pulp material and to equalize the characteristics of the sheet 104on both sides of the sheet 104. The press section 112 may include anysuitable number of press rolls in any suitable arrangement for pressingthe sheet 104.

The sheet 104 next enters a dryer section 114, which includes a seriesof heated rolls. The sheet 104 travels over the heated rolls, whichheats the sheet 104 and causes more water in the sheet 104 to evaporate.Steam or any other heated substances can be used to impart heat to theheated rolls in the dryer section 114. The dryer section 114 may includeany suitable number of heated rolls in any suitable arrangement forheating the sheet 104 and removing water from the sheet 104.

A calendar 116 processes and finishes the sheet 104. For example, thecalendar 116 may smooth the sheet 104 and impart a final finish,thickness, gloss, or other characteristic to the sheet 104. Othermaterials (such as starch or wax) can also be added to the sheet 104 toobtain the desired finish. The calendar 116 may include any suitablenumber of calendar stacks in any suitable arrangement for finishing thesheet 104. Once processing by the calendar 116 is complete, a reeldevice 118 collects the sheet 104 onto the reel 106.

This represents a brief description of one type of paper machine 102that may be used to produce a paper product. Additional detailsregarding this type of paper machine 102 are well-known in the art andare not needed for an understanding of this disclosure. Also, thisrepresents one specific type of paper machine 102 that may be used inthe system 100. Other machines or devices could be used that include anyother or additional components for producing a paper product. Inaddition, this disclosure is not limited to use with systems forproducing or processing paper products and could be used with systemsthat produce or process other items or materials, such as plastic,textiles, metal foil or sheets, or other or additional materials.

In order to control the paper-making process, the properties of thesheet 104 may be continuously or repeatedly measured and the papermachine 102 adjusted to ensure sheet quality. This control may beachieved by measuring sheet properties using a scanner 120. The scanner120 is capable of scanning the sheet 104 and measuring one or morecharacteristics of the sheet 104. For example, the scanner 120 couldcarry sensors for measuring the dry weight, moisture content, ashcontent, or any other or additional characteristics of the sheet 104.The scanner 120 includes any suitable structure or structures formeasuring or detecting one or more characteristics of the sheet 104,such as a set or array of sensors. A scanning set of sensors representsone particular embodiment for measuring sheet properties. Otherembodiments could include using a stationary set or array of sensors.

Measurements from the scanner 120 are provided to a machine direction(MD) controller 122. The controller 122 controls various operations ofthe paper machine 102 that affect machine direction characteristics ofthe sheet 104. A machine direction characteristic of the sheet 104generally refers to an average characteristic of the sheet 104 thatvaries and is controlled in the machine direction (the direction oftravel of the sheet 104). The machine direction is generallyperpendicular to the cross direction (CD) of the sheet 104 (thedirection across the sheet 104).

In this example, the controller 122 is capable of controlling the supplyof pulp to the headbox 108. For example, the controller 122 couldprovide information to a stock flow controller 124, which controls avalve 126. The stock flow controller 124 generally controls the openingand closing of the valve 126 to control the flow of stock (a mixture ofpulp, filler, water, and other materials) to the headbox 108. The stockflow controller 124 uses information from the MD controller 122 as wellas measurements of the stock flow to the headbox 108 to control thevalve 126.

The controller 122 is also capable of controlling the supply of steam tothe dryer section 114. For example, the controller 122 could provideinformation to a steam pressure controller 128, which controls a valve130. The steam pressure controller 128 generally controls the openingand closing of the valve 130 to control the steam pressure in the dryersection 114. In this way, the steam pressure controller 128 controls theheating of the rolls in the dryer section 114, thereby controlling theamount of drying provided by the dryer section 114. The steam pressurecontroller 128 uses information from the MD controller 122 as well asmeasurements of the steam pressure to control the valve 130.

The MD controller 122 includes any hardware, software, firmware, orcombination thereof for controlling the operation of a paper or othermachine. The MD controller 122 could, for example, include at least oneprocessor 132 and at least one memory 134 storing instructions and dataused, generated, or collected by the processor(s) 132.

The stock provided to the headbox 108 is produced as shown in FIG. 1B.Here, pulp is provided to a stock preparation unit 152. The stockpreparation unit 152 processes the pulp to prepare the pulp for use inmaking the sheet 104. For example, the stock preparation unit 152 couldclean and refine the pulp fibers so that the pulp fibers have desiredproperties. The stock preparation unit 152 could also receive andprocess recycled fibers recovered from the screen or mesh 110. The stockpreparation unit 152 includes any suitable structure(s) for preparingfibers or other materials for use in a paper machine.

The fibers provided by the stock preparation unit 152 are mixed with oneor more fillers and with recycled materials provided by a retention unit154. The resulting mixture represents a thick stock 158 and has arelatively high fiber consistency (such as around 4%). The thick stock158 is then mixed with white water in a short circulation path 160 toproduce a thin stock 162. The thin stock 162 has a relatively low fiberconsistency (such as around 0.2%). The thin stock 162 is provided to theheadbox 108 for use in forming the sheet 104. A long circulation path164 provides recycled material to the retention unit 154 and the stockpreparation unit 152 for recovery. The retention unit 154 may rejectsome of the material provided through the long circulation path 164.

In one aspect of operation, the MD controller 122 controls the stockflow, steam pressure, or other characteristics in the system 100. Thisallows the MD controller 122 to control various characteristics of thesheet 104. Also, the MD controller 122 can implement grade changecontrol functionality, such as by incorporating or implementing a gradechange controller 136 in the MD controller 122. The grade changecontroller 136 could also reside outside of and interact with the MDcontroller 122.

The grade change controller 136 implements grade changes in the system100 more efficiently. For example, the grade change controller 136 mayallow the paper machine 102 to transition from the production of onegrade of sheet 104 to another grade of sheet 104 more rapidly. This mayhelp to reduce or minimize the quantity of unmarketable product producedduring the grade change. Additional details regarding this grade changecontrol functionality are provided below.

Although FIGS. 1A and 1B illustrate one example of a paper productionsystem 100, various changes may be made to FIGS. 1A and 1B. For example,other systems could be used to produce or process paper products orother products. Also, while shown as including three controllers, thecontrollers could be combined or further subdivided, and the productionsystem 100 could include additional control functionality forcontrolling other aspects of the system 100. In addition, FIGS. 1A and1B illustrate one example operational environment in which grade changecontrol functionality could be implemented. The grade change controlfunctionality could be implemented in any other suitable device orsystem.

FIGS. 2A and 2B illustrate example grade change control models inaccordance with this disclosure. The grade change control models shownin FIGS. 2A and 2B are for illustration only. Other grade change controlmodels could be supported or used without departing from the scope ofthis disclosure. Also, for ease of explanation, the grade change controlmodels in FIGS. 2A and 2B are described with respect to the productionsystem 100 of FIGS. 1A and 1B. The grade change control models could beused or implemented in any other suitable device or system.

In general, the production system 100 is associated with various“process variables,” which represent various aspects of the system 100(such as speed, flow rate, or pressure). When the system 100 is used tomanufacture the sheet 104, the MD controller 122 attempts to maintain a“controlled variable” (CV) at or near a desired value or within adesired range, such as by maintaining a moisture content of the sheet104 within a specified range. The MD controller 122 attempts to maintainthe controlled variable by altering one or more “manipulated variables”(MVs), such as by adjusting an opening of a valve or a speed of thepaper machine 102. A “disturbance variable” (DV) represents a processvariable that affects a controlled variable, where the disturbancevariable can be considered by the MD controller 122 when altering themanipulated variables but generally cannot be controlled by thecontroller 122 (such as ambient temperature). By controlling certaincontrolled variables using certain manipulated variables, the MDcontroller 122 may increase or optimize the production of the sheet 104.

A grade change controller (such as the grade change controller 136 ofFIG. 1A) generally provides or implements an automatic and consistenttechnique for changing the grade of the sheet 104 produced by the papermachine 102. This may be done by coordinated changes of manipulatedvariable targets and controlled variable targets when transitioning fromone grade to another. The manipulated variables could include stockflow, machine speed, steam pressure, and headbox slice. The controlledvariables could include sheet weight, sheet moisture, and headboxjet/wire ratio.

FIG. 2A represents a part of an MD control system in its context withina process 212 (such as the paper production system 100). A controller202 represents a traditional single-variable controller C(z), such as aDahlin controller. In this example, the controller 202 receives an inputthat is based on the difference between a controlled variable setpointY_(SP) and a controlled variable measurement Y. The setpoint Y_(SP)represents the desired value of the controlled variable, and thecontrolled variable measurement Y represents the actual (measured) valueof the controlled variable in the process 212. In this example, thecontrolled variable setpoint Y_(SP) represents a desired value Y_(DV)(which may be set by an operator). The desired value Y_(DV) can then beadjusted by a controlled variable trajectory ΔY_(GC) calculated by agrade change control algorithm GC(k) 204.

The difference (or error) e between the setpoint Y_(SP) and themeasurement Y is calculated and used as an input to the controller 202.The error e is used by the controller 202 to generate an output ΔU_(SP)with the objective of minimizing the error e. The output ΔU_(SP) ispossibly corrected with a feed-forward compensation signal ΔU_(FF)associated with other manipulated variables and measurable disturbances.The resulting output is then, in this example, integrated by anintegrator 206 to form an absolute setpoint for the manipulatedvariable. The integrator 206 is represented here as an integrator in thediscrete time Z-domain.

A process operator 208 can select whether to set the manipulatedvariable setpoint U_(SP) manually or to use the integrated setpoint fromthe controller 202. In either case, a regulatory loop controller R(z)210 (which could represent another controller 124 or 128) uses theselected setpoint to determine an actuator output signal U_(OP). Theactuator output signal represents a signal provided to an actuator (suchas a valve or other type of actuator) in the production system 100,which is represented by the process P(z) 212. The actuator operates toalter the manipulated variable, thereby implementing a change that couldpossibly cause the controlled variable measurement Y to reach thecontrolled variable setpoint Y_(SP).

Prior to a grade change, the grade change control algorithm 204 maycalculate target values for the controlled and manipulated variablesbased on desired values for the next grade and other constraints. Basedon these target values, an internal process model, and the configurationof the grade change control algorithm 204, the grade change controlalgorithm 204 calculates a (theoretical) trajectory for the manipulatedvariable to transfer the controlled variable in the process 212 from theinitial grade to the desired grade. The grade change control algorithm204 also calculates a trajectory for the controlled variable.

At the grade change, the grade change control algorithm 204 updates thecurrent setpoints Y_(SP) and U_(SP) for the controlled variable andmanipulated variable, respectively. This is done by adjusting thesetpoints Y_(SP) and U_(SP) with the controlled variable trajectoryΔY_(GC) and the manipulated variable trajectory ΔU_(GC).

In a scenario with a perfect internal process model in the grade changecontrol algorithm 204, the adjustments in the manipulated variablesetpoint U_(SP) cause a change in the process 212, which may be observedwith the measurements Y. The changes in the measurements Y correspond,in this scenario, to the calculated changes in the controlled variableΔY_(GC). Hence, the setpoint Y_(SP) for the controlled variable equalsthe measurements Y for the controlled variable.

In a “real world” scenario, there is typically a difference between theactual process 212 and the internal process model in the grade changecontrol algorithm 204. There may also be disturbances in the process 212that are not captured in the internal process model of the grade changecontrol algorithm 204. The changes in measurements Y caused by theadjustments of the manipulated variable by the grade change controlalgorithm 204 may therefore not be identical to the calculated change ofmeasurements ΔY_(GC). Without any further action, the setpoint for thecontrolled variable Y_(SP) may differ or even converge from themeasurements Y of the controlled variable.

To minimize the difference between the calculated controlled variabletrajectory and the measurements Y of the controlled variable, thecontroller 202 may be used. In this case, the controller 202 works asdescribed above in parallel with the grade change control algorithm 204.The difference between the calculated controlled variable trajectory andthe measurements Y of the controlled variable cause the error e to benon-zero, and the controller 202 starts to control the process 212 viathe manipulated variable to minimize e.

The example shown in FIG. 2A may represent one of multiple controllerloops. For example, each controller loop may control one controlledvariable to its setpoint by adjusting one manipulated variable setpoint.The one manipulated variable setpoint may be adjusted by a feed-forwardsignal from one or more other controller loops. All controller loops mayshare the same grade change control algorithm 204. Even though eachcontroller loop is not multi-variable in this example, the grade changecontrol algorithm 204 can be multi-variable and thus may considercross-coupling between variables. A cross coupling is said to occur whenone manipulated variable affects more than one controlled variable. Achange in one manipulated variable to control one controlled variablemay therefore need to be compensated by adjusting other manipulatedvariable(s) to avoid undesired changes in controlled variable(s) otherthan the one intended to change.

FIG. 2B represents a part of an MD control system in its context with aprocess 262 (such as the paper production system 100). A controller 252represents a multi-variable controller [C](z), such as a PROFITcontroller from HONEYWELL INTERNATIONAL INC.

In this example, the controller 252 receives multiple inputs. Each inputis based on one of multiple setpoints Y_(1,SP), Y_(2,SP), and so on,which are associated with different controlled variables. Each setpointmay also be adjusted by one of multiple controlled variable trajectoriesΔY_(1,GC), ΔY_(2,GC), and so on, which are calculated by a grade changecontrol algorithm GC(k) 254. Based on the setpoints (or desired values),the controller 254 determines a set of manipulated variable setpointsU_(C1,SP), U_(C2,SP), and so on. Although equal in this example, thenumber of controlled variables does not have to equal the number ofmanipulated variables.

A process operator 258 can override one or more of the manipulatedvariable setpoints provided by the multivariable controller 252. A setof regulatory loop controllers 260 (which could represent othercontrollers 124 or 128) use the setpoints to determine a set of actuatoroutput signals U_(1,OP), U_(2,OP), and so on. The actuator outputsignals represent signals provided to a set of actuators (such as valvesor other type of actuators) in the production system 100, represented bythe process P(z) 262. The actuators operate to alter the manipulatedvariables, thereby implementing changes that could possibly cause thecontrolled variable measurements to reach the controlled variablesetpoints.

Prior to a grade change, the grade change control algorithm 254 maycalculate target values for the controlled and manipulated variablesbased on desired values for the next grade and other constraints. Basedon these target values, the internal process model, and theconfiguration of the grade change control algorithm 254, the gradechange control algorithm 254 calculates the (theoretical) trajectoriesfor the manipulated variables to transfer the controlled variables inthe process 262 from the initial grade to the desired grade. The gradechange control algorithm 254 also calculates trajectories for thecontrolled variables.

At the grade change, the grade change control algorithm 254 updates thecurrent setpoints (Y_(1,SP), Y_(2,SP), and so on and U_(1,SP), U_(2,SP),and so on) for the controlled variables and manipulated variables. Thiscan be done by adjusting the setpoints with the controlled variabletrajectories (ΔY_(1,GC), ΔY_(2,GC), and so on) and the manipulatedvariable trajectories (ΔU_(1,GC), ΔU_(2,GC), and so on).

In a scenario with a perfect internal process model in the grade changecontrol algorithm 254, the adjustments in the manipulated variablesetpoints cause changes in the process 262, which may be observed withthe controlled variable measurements. The changes in the measurementscorrespond, in this scenario, to the calculated changes in thecontrolled variables (ΔY_(1,GC), ΔY_(2,GC), and so on). As a result, thesetpoints for the controlled variables equal the measurements for thecontrolled variables.

In a “real world” scenario, there may be a difference between the actualprocess 262 and the internal process model in the grade change controlalgorithm 254. There may also be disturbances in the process 262 thatare not captured in the internal process model of the grade changecontrol algorithm 254. The changes in the measurements caused by theadjustments to the manipulated variables by the grade change controlalgorithm 254 may not be identical to the calculated changes to thecontrolled variables. Without any further action, the setpoints for thecontrolled variables may differ or even converge from the measurementsof the controlled variables.

To minimize the differences between the calculated controlled variabletrajectories and the measurements of the controlled variables, themulti-variable controller 252 may be used. The controller 252 may workas described above in parallel with the grade change control algorithm254. The differences between the calculated controlled variabletrajectories and the measurements of the controlled variables causeerrors to be non-zero, and the controller 252 starts to control theprocess 262 via the manipulated variables to minimize the differencesbetween the setpoints and the measured values.

Although FIGS. 2A and 2B illustrate examples of grade change controlmodels, various changes may be made to FIGS. 2A and 2B. For example,FIGS. 2A and 2B represent example control models in which a grade changecontroller could be used. However, a grade change controller could beused in any control environment represented by any suitable controlmodel. Also, while FIG. 2B illustrates the use of two controlledvariables, the grade change controller could be used in conjunction withany multi-variable controller that is controlling any number ofvariables. Further, the grade change controller could operate withoutfeedback from the process (without controlled variable measurements Y,Y₁, Y₂, etc.). This is commonly referred to as operating in “open loop.”In addition, the grade change controller could be used with any type ofMD control or without any MD controller.

FIG. 3 illustrates example tasks during a grade change in accordancewith this disclosure. For ease of explanation, the tasks in FIG. 3 aredescribed with respect to the grade change controller 136 of FIGS. 1Aand 1B implementing a grade change controller. The tasks shown in FIG. 3could be implemented in any other suitable controller.

Each grade of product produced in the production system 100 is generallyassociated with one or more different controlled variable or manipulatedvariable targets. In other words, when producing one grade of sheet 104,the MD controller 122 may operate to maintain a certain controlledvariable near one target value. When producing a different grade ofsheet 104, the MD controller 122 may operate to maintain that samecontrolled variable near a different target value. The grade changecontroller 136 implements a grade change by taking the production system100 from one operating point to another (such as from one CV or MVtarget to another) as fast and smooth as possible.

As shown in FIG. 3, the grade change controller 136 may first identifynew targets for one or more manipulated and controlled variables. Forexample, the new targets for the controlled variables can be identifiedby loading new targets from a recipe database, and the new targets forthe manipulated variables can be calculated using known controlledvariable targets. In some embodiments, new targets for the manipulatedvariables can be identified by calculating the minimum required changein the manipulated variables while ensuring that the controlledvariables reach their new targets. This could, for example, involveusing a high-fidelity non-linear process model.

Once the new manipulated and controlled variable targets have beendetermined, the grade change controller 136 generates manipulated andcontrolled variable trajectories from the targets for the current gradeto the targets for the next grade. In other words, the grade changecontroller 136 determines how to control the production system 100 tomove from the old targets to the new targets. The main objective of thegrade change controller 136 during this task may be to get allcontrolled variables from their old targets to their new targets as fastas possible.

In some embodiments, the manipulated and controlled variable targettrajectories can be identified using an iterative process. The iterativeprocess can involve the use of a linear model predictive controller(MPC) that takes hard constraints on the controlled and manipulatedvariables into account. A non-linear high-fidelity process model and alinear model parameter update function that updates the linear model inthe MPC could also be used. The linear model in the MPC could be updatedbased on the non-linear model and the current operating point (thecurrent values of the controlled and manipulated variables during aniteration). In addition, a stop condition module could be used toterminate a closed-loop target trajectory calculation.

An example of how the grade change controller 136 can be configured toiteratively perform this second task is shown in FIG. 4. Here, a linearmodel predictive controller (MPC) 402 receives differences betweencontrolled variable targets and estimated controlled variable values.The model predictive controller 402 uses this and other information togenerate new values for the manipulated variables. These manipulatedvariable values form manipulated variable trajectories. The manipulatedvariable values are also provided to a process model 404, whichrepresents the process (such as the production system 100) beingcontrolled. The process model 404 is used to determine how themanipulated variable values affect the controlled variable values. Thesecontrolled variable values form controlled variable trajectories.

The controlled variable values are provided to a process modellinearization module 406, which determines if and how models in the MPC402 are updated based on the controlled variable values produced by theprocess model. For example, the process model linearization module 406could determine how to update the gains and time delays in the model andprovide these values to the MPC 402. If the model is updated, thisprocess may be repeated. This can continue until the controlled variablevalues change by less than a specified amount.

Returning to FIG. 3, once the trajectories are determined, the gradechange controller 136 controls the production system 100 to implementthe grade change. In some embodiments, this could involve using a hardconstrained model predictive controller to adjust the operation of thepaper machine 102. However, other types of controllers could be used.

In particular embodiments, the grade change controller 136 is developedin MATLAB and is compiled into a dynamic link library (DLL). The dynamiclink library can then be called in a .NET environment.

Although FIG. 3 illustrates examples of tasks during a grade change andFIG. 4 illustrates an example of a portion of a grade change controller136, various changes may be made to FIGS. 3 and 4. For example, a gradechange could involve a larger or smaller transition between targets.Also, different trajectories could be identified for moving betweentargets. In addition, components in the grade change controller 136could be combined or omitted and additional components could be addedaccording to particular needs.

FIG. 5 illustrates an example method 500 for grade change control inaccordance with this disclosure. The embodiment of the method 500 shownin FIG. 5 is for illustration only. Other embodiments of the method 500could be used without departing from the scope of this disclosure. Also,for ease of explanation, the method 500 is described with respect to thegrade change controller 136 operating in the system 100 of FIGS. 1A and1B. The method 500 could be used by any other suitable device and in anyother suitable system.

A sheet of material having a first grade is produced at step 502. Thismay include, for example, the paper machine 102 producing a paper sheet104 having a first paper grade. This may also include the MD controller122 controlling the paper machine 102 to optimize the production of thesheet 104 having the first grade.

A grade change request is received at step 504. This could include, forexample, receiving a grade change request from an operator, an automatedgrade change request from another controller or control system, or anyother type of request from any suitable source.

New targets for the controlled variables and the manipulated variablesare identified at step 506. This may include, for example, the gradechange controller 136 identifying the new controlled variable targets ina recipe associated with the new grade. This may also include the gradechange controller 136 using the new controlled variable targets tocalculate new manipulated variable targets.

Optimal setpoint trajectories for the controlled and manipulatedvariables are identified at step 508. This may include, for example, thegrade change controller 136 performing an iterative process to identifythe setpoint trajectory that minimizes deviations between controlledvariables and their targets and that minimizes deviations betweenmanipulated variables and their targets. This may also include the gradechange controller 136 attempting to minimize the number of changes madeto the manipulated variables, attempting to minimize the total change inthe manipulated variables, and attempting to minimize the time to reachthe new controlled variable targets.

The grade change begins at step 510. This may include, for example, thegrade change controller 136 adjusting the manipulated variable setpointto the steam pressure controller 128 or the stock flow controller 124 tomake the grade change occur as fast and smooth as possible. The gradechange controller 136 uses the identified controlled and manipulatedvariable targets and trajectories to implement the grade change. Duringthe grade change, the MD controller 122 may be used to minimize thedifference between the actual and calculated trajectories for thecontrolled variables caused by model errors in the internal processmodel of the grade change controller 136 or by disturbances in theprocess 102. The setpoints for the MD controller 122 are, in that case,updated by the CV trajectories that are calculated by the grade changecontroller 136.

Once the grade change is complete, a sheet of material having a secondgrade is produced at step 514. This may include, for example, the papermachine 102 producing a paper sheet 104 having a second paper grade.This may also include the MD controller 122 controlling the papermachine 102 to optimize the production of the sheet 104 having thesecond grade.

Although FIG. 5 illustrates one example of a method 500 for grade changecontrol, various changes may be made to FIG. 5. For example, the gradechange could be initiated automatically, and no external request may berequired at step 504.

The following represents additional details regarding one specificimplementation of the grade change controller 136. These details areprovided only to describe a specific implementation of the grade changecontroller 136. Other embodiments of the grade change controller 136could be used without departing from the scope of this disclosure.

In this embodiment, the main manipulated and controlled variablesinvolved in a grade change are provided in Table 1.

TABLE 1 Manipulated Variables Units Controlled Variables Units ThickStock Flows l/min Dry Weight g/m² Filler Flows l/min Ash Percent Steampressures for kPa Moisture Percent dryer section Machine Speed m/minTo implement a grade change, the grade change controller 136 identifiesnew targets for these controlled variables using a recipe associatedwith a new grade of sheet 104 to be produced. The grade changecontroller 136 uses the new controlled variable targets to identify newtargets for these manipulated variables. In some embodiments, anoperator selects the manipulated variables for which the grade changecontroller 136 calculates new targets. In particular embodiments, anoperator may, for various production or other reasons, select the newtargets for at least some of the manipulated variables. The manipulatedvariables having targets set by an operator may be referred to as“fixed” manipulated variables, while the manipulated variables havingtargets set by the grade change controller 136 may be referred to as“free” manipulated variables.

Depending on the circumstances, the grade change controller 136 couldoperate under one of the following three scenarios:

(1) The grade change controller 136 determines targets for as manymanipulated variables as there are controlled variables;

(2) The grade change controller 136 determines more targets formanipulated variables than there are controlled variables; and

(3) The grade change controller 136 determines fewer targets formanipulated variables than there are controlled variables.

The problem of identifying new targets for the manipulated variables canbe defined as solving a set of non-linear equations, where the number ofnon-linear equations equals the number of controlled variablesconsidered. The number of controlled variables can be arbitrarydepending on the implementation. In this embodiment, as indicated inTable 1, the number of controlled variables equals three. The non-linearequations are governed by the physical relationships between themanipulated variables and the controlled variables, which can beexpressed as:

$\begin{matrix}\begin{matrix}{{y_{1} - {f_{1}\left( {K_{1},u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)}} = 0} \\{{y_{2} - {f_{2}\left( {K_{2},u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)}} = 0} \\{{y_{3} - {f_{3}\left( {K_{3},u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)}} = 0} \\\vdots \\{{y_{N_{y}} - {f_{N_{y}}\left( {K_{N_{y}},u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)}} = 0.}\end{matrix} & (1)\end{matrix}$Here, y_(i) represents the controlled variables, and u_(j) representsthe manipulated variables. Also, K_(i) represents a lumped constantassociated with physical constants and disturbance variables. Thefunctions f_(k)(•) represent the non-linear functions giving theoreticalsteady-state values for each controlled variable given the manipulatedvariables and the constants.

Depending on which of the three possible scenarios defined above isoccurring, there could be one solution, an infinite number of solutions,or no (exact) solution to the above set of Equations (1). An algorithmfor solving the set of non-linear equations used by the grade changecontroller 136 may be generic enough to handle all three scenarios. Onealgorithm for solving the set of non-linear equations involves definingand solving the following optimization problem:

$\begin{matrix}{{\min\limits_{u}{F\left( {u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)}}{s.t.\begin{matrix}{{G\left( {u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)} \leq 0} \\{{H\left( {u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)} = 0.}\end{matrix}}} & (2)\end{matrix}$The objective function F(•) is explained in detail in the followingparagraph. The inequality constraint function G(•) and the equalityconstraint function H(•) are described in more detail in subsequentparagraphs.

The objective function F(•) in Equation (2) can be partitioned into twofunctions:F(u₁,u₂, . . . ,u_(N))≡F_(CV)(u₁,u₂, . . . ,u_(N) _(u) )+F_(MV)(u₁,u₂, .. . ,u_(N) _(u) ).  (3)The first partition (F_(CV)(•)) represents the weighted sum of thequadratic difference between the target values of the controlledvariables and the calculated controlled variable values for a givenworking point (i.e. a given set of manipulated variables). That is:F_(CV)(u₁,u₂, . . . ,u_(N) _(u) )≡v₁(y_(tgt,1)−f₁(u₁,u₂, . . . ,u_(N)_(u) ))²+v²(y_(tgt,2)−f₂(u₁,u₂, . . . ,u_(N) _(u) ))²+ . . . +v_(N) _(y)(y_(tgt,N) _(y) −f_(N) _(y) (u₁,u₂, . . . ,u_(N) _(u) ))²,  (4)where v₁, v₂, . . . , v_(n) are normalization coefficients. Ideally, thevalue of this function is zero with an optimal set of manipulatedvariable targets for the next grade. This may or may not be achievable.If it is achieved, this optimal set of manipulated variable targets mayyield controlled variables equal to what an operator has set as thedesired controlled variables.

The second partition (F_(MV)(•)) represents a weighted sum of thequadratic difference between the desired target values of the “free”manipulated variables for the next grade u_(dt,k) and the target valuesof those manipulated variables. This can be expressed as:F_(MV)(u₁,u₂, . . . ,u_(N) _(u) )≡w₁(u_(dt,1)−u₁)+w₂(u_(dt,2)−u₂)²+ . .. +w_(N) _(u) (u_(dt,N) _(u) −u_(N) _(u) )².  (5)The manipulated variable target values are the optimization variables inthis optimization problem. As in the first partition, w₁, w₂, . . . ,w_(n) represent normalization coefficients.

Normalization coefficients can be used if the values of the controlledvariables are of different magnitudes or have different units comparedto each other. This might also be the case for the manipulatedvariables. Normalization coefficients are therefore used to give eachterm in Equations (4) and (5) the same relative importance. Thenormalization coefficients can be defined to penalize ratio deviationsfrom the targets, such as when:v₁≡(u_(dt,1))⁻²,v₂≡(u_(dt,2))⁻², . . . ,v_(N) _(y) ≡(u_(dt,N) _(y))⁻²  (6)andw₁≡(y_(tgt,1))⁻²,w₂≡(y_(tgt,2))⁻², . . . ,w_(N) _(u) ≡(Y_(tgt,N) _(u))⁻².  (7)

An equality constraint function (the function H(•) in Equation (2)) canalso be used depending on the current scenario. The equality constraintfunction is the same set of equations as in Equation (1). For example,if there are more manipulated variables than controlled variables, anequality constraint function may represent the set of Equations (1). Inthis case, the optimization problem is solved so that the calculatedcontrolled variable values for the next grade are equal to the desired(target) controlled variable values. Since this is an underdeterminedset of equations, there may be a degree of freedom for some manipulatedvariable values, meaning there might exist more than one set ofmanipulated variables that solves Equations (1). However, since theobjective function in Equation (5) penalizes moves in the manipulatedvariables, the solution of Equations (1) may represent the solution thatrequires the minimum amount of moves in the manipulated variables.

If there are fewer manipulated variables than controlled variables, asolution may not exist to the set of Equations (1). An equalityconstraint function may therefore not be used with this scenario. Thesolution to the optimization problem may represent the manipulatedvariable values that yield controlled variable values that are closestto the desired controlled variable values as possible in a quadraticsense.

An inequality constraint function (the function G(•) in Equation (2))can also be used. For example, non-equality constraints can be used toensure that the controlled variables and the manipulated variables arewithin their maximum and minimum limits. For the controlled variables,this can be expressed as:

$\begin{matrix}{\begin{matrix}{{{f_{1}\left( {K_{1},u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)} - y_{1,\max}} \leq 0} \\{{{f_{2}\left( {K_{2},u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)} - y_{2,\max}} \leq 0} \\\vdots \\{{{f_{N_{y}}\left( {K_{N_{y}},u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)} - y_{N_{y},\max}} \leq 0}\end{matrix}\begin{matrix}{{y_{1,\min} - {f_{1}\left( {K_{1},u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)}} \leq 0} \\{{y_{2,\min} - {f_{2}\left( {K_{2},u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)}} \leq 0} \\\vdots \\{{y_{N_{y},\min} - {f_{N_{y}}\left( {K_{N_{y}},u_{1},u_{2},\cdots\mspace{11mu},u_{N_{u}}} \right)}} \leq 0}\end{matrix}} & (9)\end{matrix}$For the manipulated variables, this can be expressed as:

$\begin{matrix}{\begin{matrix}{{u_{1} - u_{1,\max}} \leq 0} \\{{u_{2} - u_{2,\max}} \leq 0} \\\vdots \\{{u_{N_{u}} - u_{N_{u},\max}} \leq 0}\end{matrix}\begin{matrix}{{u_{1,\min} - u_{1}} \leq 0} \\{{u_{2,\min} - u_{2}} \leq 0} \\\vdots \\{{u_{N_{u},\min} - u_{N_{u}}} \leq 0.}\end{matrix}} & (10)\end{matrix}$

An example of this process is illustrated in FIG. 6. More specifically,FIG. 6 illustrates an example method 600 for controlled variable andmanipulated variable target calculation. As shown in FIG. 6, the gradechange controller 136 sets the “current” manipulated variable valuesequal to the initial manipulated variable values at step 602. Theinitial manipulated variable values may represent the actual values ofthe manipulated variables prior to a grade change.

The grade change controller 136 obtains identification strings andtarget values of any fixed manipulated variables at step 604. The gradechange controller 136 also obtains identification strings and desiredvalues of any free manipulated variables at step 606.

A paper machine process model is updated with the manipulated variablevalues at step 608. The paper machine process model may represent anon-linear model of the paper machine 102, such as a non-linear dryermodel (associated with the dryer section 114) and a non-linear dryweight model. The process model is then initialized at step 610. Thiscould include initializing the process model's state vectors and historybuffers. At step 612, an optimization solver is called to solve theoptimization problem. As described above, the optimization solver usesthe process model in its internal calculations to calculate thesteady-state values for the modeled process (i.e. the steady-statevalues of the controlled variables) given a set of manipulated variablevalues. The optimization solver “searches” for the set of manipulatedvariables minimizing the value of the objective function F(•) inEquation (2) and satisfying the constraints G(•) and H(•).

Once the target values for the manipulated variables are identified, thegrade change controller 136 identifies a set of setpoint trajectoriesfor the manipulated variables and the controlled variables. Thetrajectories ideally are used to reach the desired controlled variablevalues for the next product grade. The calculated manipulated variabletrajectories and the corresponding calculated controlled variabletrajectories can be calculated “off-line” before the actual grade changeoccurs. When the grade change is initiated, the manipulated variabletrajectories may be implemented by the MD controller 122, meaning themanipulated variable and controlled variable setpoints may be updatedwith the trajectories.

The target trajectory calculation can be formulated as a standardmulti-variable predictive controller problem. Given a specific process(process model), the MPC problem attempts to:

(1) Minimize the deviation between the controlled variable trajectoriesand the new controlled variable targets over a prediction horizon;

(2) Minimize the deviation between a set of target values for themanipulated variables and the manipulated variable trajectories over acontrol horizon; and

(3) Penalize moves in the manipulated variable trajectories.

The manipulated variable targets are the variables available for the MPCto solve the MPC problem. To be able to calculate the controlledvariables for a given set of manipulated variables, the MPC uses aprocess model. By trying to minimize the deviation between thecontrolled variable trajectories and the controlled variable targetsduring a grade change, the time for the grade change may be reduced orminimized.

In some embodiments, the MPC is implemented using a cross directionmulti-variable predictive controller (CDMPC) (such as the one describedin U.S. Pat. No. 6,807,510B1, which is hereby incorporated byreference). The MPC may use linear process models internally, and alinear process model in the MPC may be updated at every iteration step(every MPC update) with a linearized process model calculated by anon-linear model. The modeled controlled variable values from thenon-linear process model can also be used as feedback to the MPC. Themanipulated variable outputs from the MPC can be saved at each iterationstep to build the manipulated variable trajectories. The iterations maycontinue until the trajectories have converged.

The MPC uses an internal process model, and some numerical calculationsin the MPC are based on a gain matrix in the model. This matrix oftenneeds to be reconditioned to increase numerical stability. In particularembodiments, the condition number of the gain matrix in the MPC may beless than ten. Doing this may require that the gain matrix be scaled,which can be done by performing a resealing of the gain matrix before itis used in the MPC. This scaling could be represented as:G_(s)=D_(y)GD_(u) ⁻¹,  (11)where G_(s) represents the rescaled gain matrix, G represents the“original” gain matrix, and D_(y) and D_(u) represent scaling matrices.The input to the MPC and the output from the MPC may also need to berescaled. In the un-scaled case of the internal process model in theMPC, the following can be defined:y=Gu.  (12)This combined with Equation (11) may yield:

$\begin{matrix}{y = {\left. {D_{y}^{- 1}G_{s}D_{u}u}\Rightarrow\underset{\underset{y_{s}}{︸}}{D_{y}y} \right. = {G_{s}{\underset{\underset{u_{s}}{︸}}{D_{u}u}.}}}} & (13)\end{matrix}$That is:y_(s)=D_(y)yu_(s)=D_(u)u,  (14)which is the scaling of the input and output vectors. The scalingmatrices D_(y) and D_(u) can be calculated using the followingnormalization scheme:

$\begin{matrix}{\left( D_{u} \right)_{j,j} = {\left( {\sum\limits_{i = 1}^{n}\left( G_{i,j} \right)^{2}} \right)^{1/2}{\left( {G\mspace{14mu}{is}\mspace{14mu} n \times k} \right).}}} & (15)\end{matrix}$In other words, the columns are normalized by the column two-norm, whichgives D_(u). Also:

$\begin{matrix}{\left( D_{y} \right)_{i,i} = {\left( {\sum\limits_{j = 1}^{k}\left( \left( {GD}_{u}^{- 1} \right)_{i,j} \right)^{2}} \right)^{{- 1}/2}.}} & (16)\end{matrix}$Here, the rows in GD_(u) ⁻¹ are normalized by the row two-norm, givingD_(y). This is a simplified version of the scaling model discussed inU.S. Pat. No. 5,574,638 (which is hereby incorporated by reference).

A normalization may have to be introduce to give errors in thecontrolled variables and in the manipulated variables the same relativeimportance (or to give one or more properties higher importance). Threedifferent approaches to normalization of the cost coefficients could beimplemented in the algorithm:

(1) No normalization (the cost coefficients entered by the operator areused “as is”);

(2) Normalization based on the initial and target values of eachmanipulated variable and controlled variable; and

(3) Normalization based on the maximum and minimum limits of themanipulated variables and controlled variables.

Normalization based on the initial and target values of each manipulatedvariable and controlled variable could be performed as follows. Costcoefficients for deviating from the controlled variable targets can bedefined, such as by the operator. The normalizations for thesecoefficients may be based on the maximum expected error between thecontrolled variables and the controlled variable targets, withoutconsidering any overshoots. The maximum expected error is the differencebetween the initial controlled variable values and the controlledvariable targets, which can be expressed as:e _(max,k) =|y _(init,k) −y _(final,k)|.  (17)For all e_(max,k) less than one, those values can be set to one to avoiddivision by small numbers, which can be expressed as:∀e_(max,k)≦1

e _(max,k)=1  (18)The cost matrix Q_(a) can be defined as:

$\begin{matrix}{{{{diag}\; Q_{a}} = \left\lbrack {\frac{q_{a,1}}{e_{\max,1}^{2}},\frac{q_{a,2}}{e_{\max,2}^{2}},\ldots\mspace{11mu},\frac{q_{a,N_{y}}}{e_{\max,N_{y}}^{2}}} \right\rbrack},} & (19)\end{matrix}$where q_(a,k) represents the defined cost coefficients for controlledvariable deviation from the controlled variable targets. A cost matrixfor deviation from the manipulated variable targets can be created in asimilar way. The maximum expected error for the manipulated variablescan be expressed as:e _(max,k) =|u _(init,k) −u _(final,k)|.  (20)The values of e_(max,k) that are less than one can be set to one. Thecost matrix Q_(b) can be expressed as:

$\begin{matrix}{{{{diag}\; Q_{b}} = \left\lbrack {\frac{q_{b,1}}{e_{\max,1}^{2}},\frac{q_{b,2}}{e_{\max,2}^{2}},\ldots\mspace{11mu},\frac{q_{b,N_{u}}}{e_{\max,N_{u}}^{2}}} \right\rbrack},} & (21)\end{matrix}$where q_(b,k) represents the defined cost coefficients for manipulatedvariable deviation from the manipulated variable targets. Thenormalization of the cost coefficients for changes in the manipulatedvariables (i.e. cost coefficients for Δu_(k)) can be based on themaximum allowed change in the manipulated variables Δu_(max,k). The costmatrix Q_(c) can be expressed as:

$\begin{matrix}{{{{diag}\; Q_{c}} = \left\lbrack {\frac{q_{c,1}}{\Delta\; u_{\max,1}^{2}},\frac{q_{c,2}}{\Delta\; u_{\max,2}^{2}},\ldots\mspace{11mu},\frac{q_{c,N_{u}}}{\Delta\; u_{\max,N_{u}}^{2}}} \right\rbrack},} & (22)\end{matrix}$where q_(c,k) represents the defined cost coefficients for changes inthe manipulated variables.

Normalization based on the maximum and minimum limits of the manipulatedvariables and the controlled variables may be based on the maximum andminimum limits (hard constraints) of each controlled variable. These canbe expressed as:c _(a,k) =y _(max,k) −Y _(min,k).  (23)The cost matrix Q_(a) can be expressed as:

$\begin{matrix}{{{{diag}\; Q_{a}} = \left\lbrack {\frac{q_{a,1}}{c_{a,1}^{2}},\frac{q_{a,2}}{c_{a,2}^{2}},\ldots\mspace{11mu},\frac{q_{a,N_{y}}}{c_{a,N_{y}}^{2}}} \right\rbrack},} & (24)\end{matrix}$where q_(a,k) represents the defined cost coefficients for controlledvariable deviation from controlled variable targets. The normalizationin this case can be calculated in a similar way as the normalizationcoefficients for the controlled variable targets:c _(b,k) =u _(max,k) −u _(min,k),  (25)with the cost matrix:

$\begin{matrix}{{{diag}\; Q_{b}} = {\left\lbrack {\frac{q_{b,1}}{c_{b,1}^{2}},\frac{q_{b,2}}{c_{b,2}^{2}},\ldots\mspace{11mu},\frac{q_{b,N_{u}}}{c_{b,N_{u}}^{2}}} \right\rbrack.}} & (26)\end{matrix}$The normalization of the cost for changes in the manipulated variablescan be calculated in the same way as for the normalization of the costfor deviating from manipulated variable targets:c _(c,k) =u _(max,k) −u _(min,k),  (27)with the cost matrix:

$\begin{matrix}{{{diag}\; Q_{c}} = {\left\lbrack {\frac{q_{c,1}}{c_{c,1}^{2}},\frac{q_{c,2}}{c_{c,2}^{2}},\ldots\mspace{11mu},\frac{q_{c,N_{u}}}{c_{c,N_{u}}^{2}}} \right\rbrack.}} & (28)\end{matrix}$

As noted above, the process of identifying the trajectories may continuein an iterative manner until the trajectories converge. The trajectoriesmay be considered to have converged if:

(1) The differences between the controlled variable targets and thecalculated controlled variable values from the last iteration are withina “first order” limit value for all controlled variables that have thisstop condition enabled;

(2) The change in the calculated controlled variable values between twoiteration steps are within a “second order” limit value for allcontrolled variables that have this stop condition enabled;

(3) The differences between the target manipulated variable values (forthe next grade) and the manipulated variable values output from the MPCat the last iteration are within a “first order” limit value for allmanipulated variables that have this stop condition enabled; and/or

(4) The changes in the manipulated variable values output by the MPCbetween two iteration steps are within a “second order” limit value forall manipulated variables that have this stop condition enabled.

Depending on how the grade change controller 136 is configured, eachcontrolled or manipulated variable can have all, some, or none of these“stop conditions” enabled. A stop condition that is disabled may not beconsidered when the trajectory convergence is determined.

Using an MPC to minimize deviation between new targets for thecontrolled variables and calculated controlled variable trajectoriesover a prediction horizon may not give any control to the time neededfor the grade change. The time needed for the grade change may becontrolled, at least partially, by controlling the ramping of thecontrolled variables during the trajectory calculations from theirinitial values to their targets values. The length of this ramp could beset by the operator.

An example of this process is illustrated in FIG. 7. More specifically,FIG. 7 illustrates an example method 700 for variable trajectorycalculation. As shown in FIG. 7, the grade change controller 136determines whether to initialize the MPC at step 702. Initialization maybe required, for example, if this is the first iteration of the method700 or if the MPC has been reset. If initialization is required, the MPCis initialized with the current (pre-grade change) manipulated andcontrolled variable setpoints at step 704.

If the option to use controlled variable target ramping is set, thecontrolled variable targets to be used by the MPC in this iteration areupdated at step 706. The MPC is then updated (executed) one time withthe simulated controlled variable values from the last trajectorycalculation iteration as an input (or the initial controlled variablevalues if it is the first iteration of the trajectory calculation) tosimulate controller outputs at step 708. The outputs from the MPCrepresent simulated manipulated variable values. The non-linear processmodel is then updated with these manipulated variable values to generatesimulated controlled variable values at step 710. The process gains atthe working point (the state of the simulated process) are alsocalculated during this step. The MPC is updated with the new processgains at step 712.

The trajectories are checked for convergence at step 714. If thetrajectories are determined to have converged, a “finished” flag is setat step 716, and the method 700 ends. Otherwise, a check is performed todetermine if the maximum number of iterations of the trajectorycalculation has been reached at step 718. If so, the “finished” flag iscleared at step 720, and the method 700 ends. This indicates that themethod 700 is ending without the trajectories converging. If moreiterations are possible, a check is made to determine if a “manualiterations” option is set at step 722. If this option is set, anindication that more iterations are required is set at step 724, and themethod 700 ends regardless whether the trajectories have converged. Thevariables used by the trajectory calculation can be kept persistence inmemory so the method 700 can be called again to perform the nextiteration if an operator initiates additional iterations.

An example method for initializing the MPC (such as during step 704) isshown in FIG. 8. Cost matrices to be used in the MPC are calculated atstep 802. Data structures used in the call to the MPC are set up withoperator-specified or other configuration data at step 804. A non-linearprocess model (not the internal linear process model in the MPC) isinitialized at step 806.

The non-linear process model is updated with the initial (pre-gradechange) manipulated variable values at step 808. The process model thenyields the (modeled) steady-state controlled variable values based onthe given manipulated variable values. These controlled variable valuesmay be used later during MPC initialization.

The process gains and the time delays in the MPC's internal processmodel are updated with the process gains and time delays calculated bythe non-linear process model at step 810. The MPC builds state-spacematrices for its internal process model at step 812, and the MPC buildsprediction matrices at step 814. The MPC builds cost matrices (QPmatrices) at step 816, and the MPC is initialized at step 818.

An example method for updating the MPC (such as during step 708) isshown in FIG. 9. A determination is made at step 902 whether an optionto use a non-linear model is set. If so, the internal process model inthe MPC is updated with a linearized process model from the latest modelupdate. This may include obtaining a linearized process model from thenon-linear model at step 904, updating the internal process model in theMPC with the new linearized process model at step 906, and building newstate-space matrices for the MPC based on the updated process model atstep 908.

A determination is made at step 910 whether only an update of the statesof the MPC process model is to be performed. Depending on thisdetermination, “Controller Available” flags are set or cleared. Forexample, if only a state update is being performed, all “ControllerAvailable” flags may be set to zero at step 912. If a full controllerupdate is being performed, the “Control Available” flags are set to whatmanipulated variables are actually available for control at step 914. Atthat point, the CDPMC controller is updated at step 916.

The above description and its associated figures have described andillustrated various aspects of one particular implementation of thegrade change controller 136. Other embodiments of the grade changecontroller 136 could be used without departing from the scope of thisdisclosure.

In some embodiments, various functions described above are implementedor supported by a computer program that is formed from computer readableprogram code and that is embodied in a computer readable medium. Thephrase “computer readable program code” includes any type of computercode, including source code, object code, and executable code. Thephrase “computer readable medium” includes any type of medium capable ofbeing accessed by a computer, such as read only memory (ROM), randomaccess memory (RAM), a hard disk drive, a compact disc (CD), a digitalvideo disc (DVD), or any other type of media.

It may be advantageous to set forth definitions of certain words andphrases used throughout this patent document. The term “couple” and itsderivatives refer to any direct or indirect communication between two ormore elements, whether or not those elements are in physical contactwith one another. The terms “include” and “comprise,” as well asderivatives thereof, mean inclusion without limitation. The term “or” isinclusive, meaning and/or. The phrases “associated with” and “associatedtherewith,” as well as derivatives thereof, may mean to include, beincluded within, interconnect with, contain, be contained within,connect to or with, couple to or with, be communicable with, cooperatewith, interleave, juxtapose, be proximate to, be bound to or with, have,have a property of, or the like. The term “controller” means any device,system, or part thereof that controls at least one operation. Acontroller may be implemented in hardware, firmware, software, or somecombination of at least two of the same. The functionality associatedwith any particular controller may be centralized or distributed,whether locally or remotely.

While this disclosure has described certain embodiments and generallyassociated methods, alterations and permutations of these embodimentsand methods will be apparent to those skilled in the art. Accordingly,the above description of example embodiments does not define orconstrain this disclosure. Other changes, substitutions, and alterationsare also possible without departing from the spirit and scope of thisdisclosure, as defined by the following claims.

1. A method comprising: identifying a target for at least one controlledvariable and a target for at least one manipulated variable, the atleast one manipulated variable and the at least one controlled variableassociated with production of a product; calculating a trajectory forthe at least one manipulated variable and a corresponding trajectory forthe at least one controlled variable, the trajectories calculated usingthe targets and at least one equation that minimizes, for thetrajectories, at least one of: a number of changes made to the at leastone manipulated variable, a total change to the at least one manipulatedvariable, and a time to reach the variable targets; and implementing agrade change using the trajectories so as to transition from productionof the product having a first grade to production of the product havinga second grade.
 2. The method of claim 1, wherein: the product comprisesa paper sheet produced by a paper machine; the at least one controlledvariable comprises one or more of: a dry weight of the paper sheet, anash content of the paper sheet, and a moisture content of the papersheet; and the at least one manipulated variable comprises one or moreof: a thick stock flow, a filler flow, a steam pressure associated witha dryer section in the paper machine, and a machine speed associatedwith the paper machine.
 3. The method of claim 1, wherein: identifyingthe target for the at least one controlled variable comprises using arecipe associated with the second grade; and identifying the target forthe at least one manipulated variable comprises using the target for theat least one controlled variable.
 4. The method of claim 1, whereincalculating the trajectories comprises performing an iterative processin order to identify the trajectory for the at least one manipulatedvariable that: minimizes deviations between each controlled variable andits target; minimizes deviations between each manipulated variable andits target; and minimizes the number of changes to each manipulatedvariable.
 5. The method of claim 4, wherein performing the iterativeprocess comprises: calculating values for the at least one manipulatedvariable, the values forming the trajectory for the at least onemanipulated variable; calculating corresponding values for the at leastone controlled variable, the corresponding values forming the trajectoryfor the at least one controlled variable; updating a process model usedto identify the corresponding values for the at least one controlledvariable; and repeating the calculating and updating steps until atleast stop condition occurs.
 6. The method of claim 5, wherein the atleast one stop condition comprises one or more of: a difference betweenthe target for the at least one controlled variable and the calculatedvalue for the at least one controlled variable from a precedingiteration is within a first limit; a change in the calculated values forthe at least one controlled variable between two consecutive iterationsis within a second limit; a difference between the target for the atleast one manipulated variable and the calculated value for the at leastone manipulated variable from a preceding iteration is within a thirdlimit; and a change in the calculated values for the at least onemanipulated variable between two consecutive iterations is within afourth limit.
 7. The method of claim 1, wherein implementing the gradechange comprises adjusting operation of at least one processing orproduction component so that actual values of the at least onemanipulated variable and the at least one controlled variable match orapproximate the trajectories.
 8. An apparatus comprising: at least oneprocessor operable to: identify a target for at least one controlledvariable and a target for at least one manipulated variable, the atleast one manipulated variable and the at least one controlled variableassociated with production of a product; calculate a trajectory for theat least one manipulated variable and a corresponding trajectory for theat least one controlled variable using the targets and at least oneequation that minimizes, for the trajectories, at least one of: a numberof changes made to the at least one manipulated variable, a total changeto the at least one manipulated variable, and a time to reach thevariable targets; and implement a grade change using the trajectories soas to transition from production of the product having a first grade toproduction of the product having a second grade; and at least one memoryoperable to store the targets and the trajectories.
 9. The apparatus ofclaim 8, wherein: the product comprises a paper sheet produced by apaper machine; the at least one controlled variable comprises one ormore of: a dry weight of the paper sheet, an ash content of the papersheet, and a moisture content of the paper sheet; and the at least onemanipulated variable comprises one or more of: a thick stock flow, afiller flow, a steam pressure associated with a dryer section in thepaper machine, and a machine speed associated with the paper machine.10. The apparatus of claim 8, wherein: the at least one processor isoperable to identify the target for the at least one controlled variableusing a recipe associated with the second grade; and the at least oneprocessor is operable to identify the target for the at least onemanipulated variable using the target for the at least one controlledvariable.
 11. The apparatus of claim 8, wherein the at least oneprocessor is operable to calculate the trajectories by: calculatingvalues for the at least one manipulated variable, the values forming thetrajectory for the at least one manipulated variable; calculatingcorresponding values for the at least one controlled variable, thecorresponding values forming the trajectory for the at least onecontrolled variable; updating a process model used to identify thecorresponding values for the at least one controlled variable; andrepeating the calculating and updating steps until at least stopcondition occurs.
 12. The apparatus of claim 11, wherein the at leastone stop condition comprises one or more of: a difference between thetarget for the at least one controlled variable and the calculated valuefor the at least one controlled variable from a prior iteration iswithin a first limit; a change in the calculated values for the at leastone controlled variable between two consecutive iterations is within asecond limit; a difference between the target for the at least onemanipulated variable and the calculated value for the at least onemanipulated variable from a prior iteration is within a third limit; anda change in the calculated values for the at least one manipulatedvariable between two consecutive iterations is within a fourth limit.13. The apparatus of claim 8, wherein the at least one processor isoperable to implement the grade change by adjusting operation of atleast one processing or production component so that actual values ofthe at least one manipulated variable and the at least one controlledvariable match or approximate the trajectories.
 14. The apparatus ofclaim 13, wherein: the at least one processing or production componentis controlled by at least one controller; and the at least one processoris operable to adjust the operation of the at least one processing orproduction component by altering at least one control signal generatedby the at least one controller.
 15. A computer readable medium embodyinga computer program, the computer program comprising computer readableprogram code for: identifying a target for at least one controlledvariable and a target for at least one manipulated variable, the atleast one manipulated variable and the at least one controlled variableassociated with production of a product; calculating a trajectory forthe at least one manipulated variable and a corresponding trajectory forthe at least one controlled variable, the trajectories calculated usingthe targets and at least one equation that minimizes, for thetrajectories, at least one of: a number of changes made to the at leastone manipulated variable, a total change to the at least one manipulatedvariable, and a time to reach the variable targets; and implementing agrade change using the trajectories so as to transition from productionof the product having a first grade to production of the product havinga second grade.
 16. The computer readable medium of claim 15, wherein:the product comprises a paper sheet produced by a paper machine; the atleast one controlled variable comprises one or more of: a dry weight ofthe paper sheet, an ash content of the paper sheet, and a moisturecontent of the paper sheet; and the at least one manipulated variablecomprises one or more of: a thick stock flow, a filler flow, a steampressure associated with a dryer section in the paper machine, and amachine speed associated with the paper machine.
 17. The computerreadable medium of claim 15, wherein: the computer readable program codefor identifying the target for the at least one controlled variablecomprises computer readable program code for using a recipe associatedwith the second grade; and the computer readable program code foridentifying the target for the at least one manipulated variablecomprises computer readable program code for using the target for the atleast one controlled variable.
 18. The computer readable medium of claim15, wherein the computer readable program code for calculating thetrajectories comprises: computer readable program code for calculatingvalues for the at least one manipulated variable, the values forming thetrajectory for the at least one manipulated variable; computer readableprogram code for calculating corresponding values for the at least onecontrolled variable, the corresponding values forming the trajectory forthe at least one controlled variable; computer readable program code forupdating a process model used to identify the corresponding values forthe at least one controlled variable; and computer readable program codefor repeating the calculating and updating steps until at least stopcondition occurs.
 19. The computer readable medium of claim 15, whereinthe computer readable program code for implementing the grade changecomprises computer readable program code for adjusting operation of atleast one processing or production component so that actual values ofthe at least one manipulated variable and the at least one controlledvariable match or approximate the trajectories.
 20. A system,comprising: a paper machine operable to produce a paper sheet havingmultiple grades; and a controller operable to initiate a transition froma first grade to a second grade by: identifying a target for at leastone controlled variable and a target for at least one manipulatedvariable; calculating a trajectory for the at least one manipulatedvariable and a corresponding trajectory for the at least one controlledvariable using the targets and at least one equation that minimizes, forthe trajectories, at least one of: a number of changes made to the atleast one manipulated variable, a total change to the at least onemanipulated variable, and a time to reach the variable targets; andimplement a grade change using the trajectories so as to transition fromproduction of the paper sheet having the first grade to production ofthe product having the second grade.